The quantum hydrodynamic representation in curved space (original) (raw)
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The quantum hydrodynamic representation in curved space and the related Einstein equation
2017
The work shows that the evolution of quantum states in the hydrodynamic representation can be obtained by Lagrangean motion equations that can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been generalized in the non-Euclidean space-time by using the physics covariance postulate, the quantum gravity equation, determining the geometry of the space-time necessary to give full meaning to them, is obtained by minimizing the overall action comprehending the gravitational field. The theoretical output for a scalar uncharged field shows the spontaneous emergence of a cosmological energy impulse tensor density (CEITD) that in the classical limit converges to a constant. The mean value of CEITD in the galactic space leads to the correct order of magnitude of the cosmological constant. The coupling of the quantum gravitational equation with half-spin fermions is finally developed.
2017
In this work the scalar free Klein-Gordon field coupled to the quantum mechanical gravity equation (QMGE), that takes into account the quantum property of matter, is quantized. The model has been developed at the first order in the metric tensor with a self-consistent analytical dependence of the energy impulse tensor by the quantum field. The quantum behavior, due to the quantum potential energy, in the gravity equation (GE) has been investigated by studying the energy-impulse tensor density generated the quantum field. The outputs of the theory show that the vacuum energy density of the zero point is effective for the cosmological constant only in the volume of space where the mass is localized in particles or in high gravity bodies, leading to a cosmological effect on the motion of the galaxies that is compatible with the astronomical observations. The paper shows that the energy-impulse tensor density makes the QMGE, in the quasi-Euclidean limit, physically independent by the le...
Hydrodynamic representation and energy balance for Dirac and Weyl fermions in curved space-times
The European Physical Journal C
Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac–Euler equations for fermions involving a continuity equation and a first integral of the Bernoulli equation. Comparing between the Dirac and Klein–Gordon equations we obtain the balance equation for fermion particles. We also use the correspondence between fermions and bosons to derive the hydrodynamic representation of the Weyl equation which is a chiral form of the Dirac equation.
arXiv (Cornell University), 2017
The work shows that the evolution of the field of the free Klein-Gordon equation, in the hydrodynamic representation, can be obtained by Lagrangean motion equations that can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been generalized in the non-Euclidean space-time by using the physics covariance postulate, the quantum gravity equation, determining the geometry of the space-time necessary to give full meaning to them, is obtained by minimizing the overall action comprehending the gravitational field. The theoretical output for a scalar uncharged field shows the spontaneous emergence of the cosmological energy impulse tensor density (CEITD) in the gravity equation. The scalar free Klein-Gordon field coupled to the gravity equation (GE), with the analytical dependence of the energy impulse tensor as a function of the field, is quantized at the first order in the metric tensor. The cosmological constant (CC), generated the quantum field, has been investigated and calculated for the vacuum. The outputs of the theory show that the vacuum energy density of the zero point is effective for the cosmological constant only in the volume of space where the mass is localized in particles or in high gravity bodies, leading to a cosmological effect on the motion of the galaxies that is compatible with the astronomical observations. The paper shows that, in the quasi-Euclidean limit, the energy-impulse tensor density makes the GE asymptotically independent by the zero-point energy density of the vacuum, and possibly compatible with the renormalization techniques of the QFT.
The gravity of the classical field of quantum mechanics
2020
In this work, with the help of the quantum hydrodynamic formalism, the gravitational equation associated to the Dirac field is derived. The hydrodynamic representation of the Dirac equation have been generalizaed to the curved space-time in the covariant form. Thence, the metric of the spacetime has been defined by imposing the minimum action principle. The derived gravity shows the spontaneous emergence of the cosmological gravity tensor (CGT) as a part of the energy-impulse tensor density (EITD) that in the classical limit leads to the cosmological constant (CC). Even if the classical cosmological constant is set to zero, the CGT is non zero, allowing to have a stable quantum vacuum (out of the collapsed branched polymer phase). The theory shows that in the classical limit, the gravity equation leads to the general relativity equation. In the perturbative approach, the CGT leads to a second order correction to the Newtonian gravity that takes contribution from the space where the ...